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In physics, thermalisation (or thermalization) is the process of physical bodies reaching thermal equilibrium through mutual interaction. In general, the natural tendency of a system is towards a state of equipartition of energy and uniform temperature that maximizes the system's entropy .
In physics, the Fermi–Pasta–Ulam–Tsingou (FPUT) problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi–Pasta–Ulam–Tsingou recurrence (or Fermi–Pasta–Ulam recurrence) – instead of the expected ergodic behavior.
The phenomenon, when taken to mean "hot water freezes faster than cold", is difficult to reproduce or confirm because it is ill-defined. [4] Monwhea Jeng proposed a more precise wording: "There exists a set of initial parameters, and a pair of temperatures, such that given two bodies of water identical in these parameters, and differing only in initial uniform temperatures, the hot one will ...
This is an energy balance which defines the position of the moving interface. Note that this evolving boundary is an unknown (hyper-)surface; hence, Stefan problems are examples of free boundary problems. Analogous problems occur, for example, in the study of porous media flow, mathematical finance and crystal growth from monomer solutions. [1]
The eigenstate thermalization hypothesis says that for an arbitrary initial state, the expectation value of ^ will ultimately evolve in time to its value predicted by a microcanonical ensemble, and thereafter will exhibit only small fluctuations around that value, provided that the following two conditions are met: [4]
This process of "quantum thermalization" may be understood in terms of B acting as a reservoir for A. In this perspective, the entanglement entropy S = − Tr ( ρ A log ρ A ) {\displaystyle S=-\operatorname {Tr} (\rho _{A}\log \rho _{A})} of a thermalizing system in a pure state plays the role of thermal entropy.
CMB spectral distortions are tiny departures of the average cosmic microwave background (CMB) frequency spectrum from the predictions given by a perfect black body.They can be produced by a number of standard and non-standard processes occurring at the early stages of cosmic history, and therefore allow us to probe the standard picture of cosmology.
For examples, glass manufacturer Schott provides the coefficient of linear thermal expansion for a temperature range of -30 C to 70 C. The change in length of a material is a function of the change in temperature with respect to the standard measurement temperature, T 0 {\textstyle T_{0}} .